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hw5soln - PADP 8670 Fall 201 l Fertig UGA Homework 5...

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Unformatted text preview: PADP 8670 Fall 201 l Fertig UGA Homework 5 Solutions 1. The demand function for cigars is PrZKlO-ZQ and the supply function is P=3+Q, where P is the price per box and Q is the number ofboxes. Cigars are taxed at $4 per box. a. Draw the supply and demand before and after the tax is imposed, indicating with actual numbers the quantities and prices before and after the tax. S=D: 240-2Q=3+Q 23723Q Z430 P=3+79 Zap P=82 Before tax: P After tax: git—.57 New demand: 8 Pz236-2Q - 236—2Q=3+Q 302/3 233=3Q 0:77.67 ,5 _ ‘ P s =3+77.67 " P s =80.67 777; 7&l l20 61 P d 280.6744 P d =84.67 b. Do consumers and suppliers share the cost ofthe tax equally? Ifnot, what share do they each pay? No. Consumers pay $84.67~$82=$2.67 ofthe $4 tax: about 67% Producers pay $82-$80.67=$1.33 of the $4 tax: about c. Given your answer to [a], is the price elasticity of demand elastic or inelastic? Since consumers pay more of the tax, the price elasticity of demand is -. Producers pass on a lot ofthe tax to consumers because they know consumers are not very price sensitive. 2. Assume that the demand for bread is Q=4-5-4-P and the supply of bread is Qx15+8P, Where P is the price ofa loafand Q is the number ofloaves of bread. Assume that the government wants to ensure that the price of bread never rose above $2 per loaf. The policy proposed is to pay bakers enough ofa subsidy for each loafofbread so that the price is $2 per loaf. How much would the subsidy per loafhave to be? Make sure to draw a graph ofthe supply and demand before and after the subsidy is given, indicating with actual numbers the quantities and prices before and after the subsidy. Demand: P Q=4—5-4P 4P=45-Q ll 1”: P:11.25 -— Q/4 Supply: Q=15+8 8P=Q-15 P:-1.875+Q/8 U! ”all; \ 45-4P=15+8P 2.75 _ S w/subswlfi 30:1 P 25 '. P=2.5 Z Q:45-4*2.5 IfP=$2. then 16%: ”| $76 Q d =45-4*2 “7-995 To figure out subsidy amount, what price would suppliers need to supply 37 units? 37:15+8P 22=8P P=2.75 So, subsidy must be $2.75~$2-. Alternate approach: To figure out subsidy amount, figure out what new supply curve intercept would be to get an intersection of the new supply curve and the demand curve at $2 and 37 loaves. New supply curve: P=-1.8’75+s+Q/8 Demand curve: P=11.25-Q/4— 52D, plug in Q=37 and solve for s: -1.875+s+37/8=11.25-37/4 s=11.25-9.25+1.875-4.625 ...
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